A woman who was seen exercising in the neighborhood around the time that the head of Colorado's prison system was fatally shot in his home could be a key witness in the murder investigation, authorities said today.

Tom Clements, 58, was shot to death around 8:30 p.m. Tuesday. Initial reports said the director of the State Department of Corrections had been shot when he answered the door at his Monument, Colo., home, but authorities said this afternoon that they were unable to confirm the sequence of events or a motive for the shooting.

"Because of the fact Mr. Clements served in the position he did, we're sensitive to the fact there could be any number of people who have a motive," Lt. Jeff Kramer, a spokesman for the El Paso County Sheriff's office, said at a news conference this afternoon.

He also said authorities were keeping an open mind and had not yet ruled out whether Clements was the victim of a random shooting.

With few leads to go on, authorities are hoping the woman who was seen speed-walking in the neighborhood Tuesday night will come forward. She was described by witnesses as being between the ages of 35 and 50 and was dressed in a hat, dark wind-breaker and white pants, Kramer said.

Police canvassed the neighborhood and found a witness who noticed a suspicious vehicle parked one street beyond Clements' home and put the time just before Clements' family called 911 to report the shooting, police said today.

"The vehicle was observed by this resident parked there, but it was running at the time," Lt. Kramer said. "Two to three minutes later that vehicle was gone. Then, two minutes after that -- we're up to 8:37 p.m. -- that same local resident saw the vehicle traveling westbound."

Kramer said authorities believe the woman who was exercising might have seen the vehicle and that authorities are "eager" to speak with her.

The vehicle, which had its green dashboard lights on while parked, was described as a two door, dark colored, 1990s model similar to a Lincoln.

Police continue going house to house trying to find out what neighbors heard and saw, and K-9 units were deployed to see whether they could locate anything that might be helpful in the investigation.

Colorado Gov. John Hickenlooper struggled to hold back tears today while speaking to reporters this morning and conceded that little is known about a suspect or motive.

"It's an active investigation. We don't know anything -- or enough -- at this point," he said.

Hickenlooper was scheduled to sign legislation today that will place new limits on ammunition magazines and expands background checks for firearms. The new legislation is seen as a response to a string of mass shootings across the country, one of the worst of which was the Aurora, Colo., shooting in July 2012 that left 12 dead and injured 58.

Speaking today, Hickenlooper reflected on Clements' career and time working within Colorado government. Clements was appointed head of Colorado's Department of Corrections in 2011 by Hickenlooper, after serving 31 years in the Missouri Department of Corrections.

"We lured Tom away," Hickenlooper said. "He was far and away the best choice we could find in the country. He understood the idea of building a team and operating an enterprise. … His unfailing good nature would come through and everything he did."

Clements is survived by his wife, Lisa Clements, and his two daughters.

His family released a statement this afternoon mourning the "devoted husband and beloved father."

"There are no words at this time to describe our grief and loss," they said. "We thank our friends and those praying for us here and across the nation. Your well-wishes and prayers bring us strength. We appreciate your continued respect for our privacy during this terrible loss."